Question: Reduce to lowest terms: $- \dfrac{6}{5} \div - \dfrac{4}{7} = {?}$
Explanation: Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $- \dfrac{4}{7}$ is $- \dfrac{7}{4}$ Therefore: $ - \dfrac{6}{5} \div - \dfrac{4}{7} = - \dfrac{6}{5} \times - \dfrac{7}{4} $ $ \phantom{- \dfrac{6}{5} \times - \dfrac{7}{4}} = \dfrac{-6 \times -7}{5 \times 4} $ $ \phantom{- \dfrac{6}{5} \times - \dfrac{7}{4}} = \dfrac{42}{20} $ The numerator and denominator have a common divisor of $2$, so we can simplify: $ \dfrac{42}{20} = \dfrac{42 \div 2}{20 \div 2} = \dfrac{21}{10} $